Derived from a general definition of texture in a local neighborhood, local directional pattern (LDP) encodes the directional information in the small local 3x3 neighborhood of a pixel, which may fail to extract detailed information especially during changes in the input image due to illumination variations. Therefore, in this paper we introduce a novel feature extraction technique that calculates the nth order direction variation patterns, named high order local directional pattern (HOLDP). The proposed HOLDP can capture more detailed discriminative information than the conventional LDP. Unlike the LDP operator, our proposed technique extracts nth order local information by encoding various distinctive spatial relationships from each neighborhood layer of a pixel in the pyramidal multi-structure way. Then we concatenate the feature vector of each neighborhood layer to form the final HOLDP feature vector. The performance evaluation of the proposed HOLDP algorithm is conducted on several publicly available face databases and observed the superiority of HOLDP under extreme illumination conditions.